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The complex domain adaptive filtering algorithms has shown excellent performance in the field of signal processing. Among them, the well-known complex least mean square (CLMS) algorithm has been widely used in practical projects. However, the CLMS algorithm only considers the case where the output signal is disturbed by noise, ignores the input signal may also be interfered by noise. Moreover, the signal is likely to be disturbed by impulsive noise in practice. Based on the above problems, the complex total least mean M-estimation (CTLMM) adaptive algorithm based on the M-estimation function is put forward in this paper. The algorithm can well handle the case where both input and output signals are subject to complex domain noise interference, and it also shows robustness with impulsive noise. This paper also analyzes the local stability of the CTLMM algorithm and discuss the theoretical steady-state error of the algorithm. Finally, simulation results verify the advantages of CTLMM algorithm and the rightness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

• The TLS-APL algorithm is proposed by using the gradient descent method and the unconstrained optimization method, which solves the problem of overall performance degradation of the APL algorithm in the EIV model. • By using some common assumptions, the local extremum of the TLS-APL algorithm is analyzed. Therefore, the expected parameter is the optimal value of the iterative estimation and fully demonstrates the correctness of the iterative update. • The mean, mean square, and steady-state MSD performance of the TLS-APL algorithm is derived by using the Kronecker product and vec operator respectively. In addition, the fitting effects of theoretical steady-state MSD curves and actual steady-state MSD curves under different parameters are analyzed, which proves the rationality of theoretical derivation. • The VSS method is presented from the maximum decrease of MSD from the current iteration to the next iteration. Compared to the TLS-APL algorithm with a fixed step size, the VSS-TLS-APL algorithm with the VSS method has both fast convergence speed and low steady-state error. In the errors-in-variables (EIV) model, the steady state characteristics of the affine-projection-like (APL) algorithm are poor. Hence, the total least squares APL (TLS-APL) algorithm different from the bias-compensated is proposed, which can reduce the adverse influence of input and output noise on weight update. Then, the local extremum of the TLS-APL algorithm is verified, that is, the expected parameter is the optimal value of the iterative estimation. Moreover, the mean, mean square, and steady-state mean square deviation (MSD) performance of the proposed TLS-APL algorithm are deduced by using the Kronecker product and vec operator, respectively. To balance the convergence characteristics and steady-state characteristics, the step size optimization of the TLS-APL algorithm, namely the variable step size TLS-APL (VSS-TLS-APL) algorithm, is derived from the analysis of MSD. Considering the existence of gradient errors, the fitting effects of theoretical steady-state MSD curves and actual steady-state MSD curves under different parameters are analyzed separately, which proves the rationality of theoretical derivation. In addition, the VSS-TLS-APL algorithm with optimized step size is compared with the TLS-APL algorithm with fixed step size in the application of system identification, and the effect of the variable step size (VSS) is verified. The experiments of system identification and acoustic echo cancelation prove that the VSS-TLS-APL algorithm is superior to the existing known algorithms. [ABSTRACT FROM AUTHOR]

To improve the performance of the diffusion Huber-based normalized least mean square algorithm in the presence of impulsive noise, this paper proposes a distributed recursion scheme to adjust the thresholds. Because of the decreasing characteristic of the thresholds, the proposed algorithm can also be interpreted as a robust diffusion normalized least mean square algorithm with variable step sizes so that it has not only fast convergence but also small steady-state estimation error. Based on the contaminated Gaussian model, we analyze the mean square behavior of the algorithm in impulsive noise. Moreover, to ensure good tracking capability of the algorithm for the sudden change of parameters of interest, a control strategy is given that resets the thresholds with their initial values. Simulations in various noise scenarios show that the proposed algorithm performs better than many existing diffusion algorithms. [ABSTRACT FROM AUTHOR]

• The variable step-size widely linear complex-valued NLMS (VSS-WL-CNLMS) algorithm which is applicable to the case of highly correlated input is proposed, where the variable step-size (VSS) is derived by minimizing the mean-square deviation (MSD). • The proposed VSS-WL-CNLMS algorithm is convergent in the mean square sense. • Based on the approximate uncorrelating transform and Rayleigh distribution, the theoretical transient and stead-state behaviors of the VSS-WL-CNLMS algorithm are analyzed in detail. The shrinkage widely linear complex-valued least mean square (SWL-CLMS) algorithm with a variable step-size (VSS) overcomes the tradeoff between fast convergence and low steady-state misalignment, but meanwhile suffers from instability for highly correlated input signals because of the gradient noise amplification problem. To obtain a VSS that is also applicable to the case of highly correlated input signals, in this paper, we propose the VSS widely linear complex-valued normalized least mean square (VSS-WL-CNLMS) algorithm, where the VSS is derived by minimizing the mean-square deviation (MSD). Owing to the normalization, the VSS-WL-CNLMS algorithm is convergent in the mean square sense. By using the Rayleigh distribution, we calculate the mean step-size, which is then combined with the approximate uncorrelating transform to analyze the transient and steady-state mean square error (MSE) behaviors. Simulations for system identification scenario show that the proposed VSS-WL-CNLMS algorithm outperforms some well-known techniques and verify the accuracy of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Highlights • We propose an improved diffusion total least-squares (DTLS) algorithm, where the estimated value at each node is passed through a first order recursive filter with adjustable parameter in order to enhance the identification performance. • We develop robust adaptive strategies to update various internal system parameters of the proposed DTLS algorithm. • The convergence behavior of the adaptive weight vector and related system parameters of the new algorithm are analyzed by means of Lyapunov stability theory. • Simulation results in the context of distributed system identification demonstrate the superiority of the proposed DTLS algorithm. Abstract The errors-in-variables (EIV) system model has been widely studied under the assumption that both input and output signals are contaminated with noise. For the in-network distributed linear system identification problem under the EIV model, the total least-squares (TLS) approach which has the ability to minimize perturbations in both input and output signals offers an efficient solution. In this paper, we propose an improved diffusion total least-squares algorithm, where the estimated (i.e. filtered) value at each node is passed through a first order recursive filter with adjustable parameter in order to enhance the identification performance. The resulting outputs from all the nodes are subsequently used to adapt the unknown linear system weight vector in real-time through a cooperative diffusion scheme based on the adapt-then-combine (ATC) policy. We also present robust adaptive strategies to tune various internal system parameters, such as the steps sizes, normalization factors, etc., under practical conditions of operation. The convergence behavior of the adaptive weight vector and related system parameters is analyzed by employing Lyapunov stability theory. Simulation results for various distributed system identification scenarios demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The active noise control (ANC) based on the principle of superposition is an attractive method to attenuate the noise signals. However, the impulsive noise in the ANC systems will degrade the performance of the controller. In this paper, a filtered-x recursive maximum correntropy (FxRMC) algorithm is proposed based on the maximum correntropy criterion (MCC) to reduce the effect of outliers. The proposed FxRMC algorithm does not requires any priori information of the noise characteristics and outperforms the filtered-x least mean square (FxLMS) algorithm for impulsive noise. Meanwhile, in order to adjust the kernel size of FxRMC algorithm online, a recursive approach is proposed through taking into account the past estimates of error signals over a sliding window. Simulation and experimental results in the context of active impulsive noise control demonstrate that the proposed algorithms achieve much better performance than the existing algorithms in various noise environments. [ABSTRACT FROM AUTHOR]

To solve the problem that the performance of maximum total correntropy (MTC) algorithm is limited by kernel width, a more flexible algorithm called maximum mixture total correntropy (MMTC) is proposed in this brief, which is derived by combining the mixture correntropy (MC) and total least square (TLS) method. Then, the local mean and mean square performance of the MMTC algorithm are analyzed in detail under some simplifying assumptions, the stable step size range and theoretical steady-state MSD expression are also given. Numerical simulations exhibit that the MMTC performs better than MTC for the parameter estimation of the error-in-variable (EIV) model in the background of impulse noise, the validity of the theoretical analysis is also verified. [ABSTRACT FROM AUTHOR]

Abstract: In actual nonlinear active noise control (NANC) systems, there often exist nonlinear distortions in such cases: the primary path may be nonlinear, the reference noise may exhibit nonlinear distortion, and the secondary path may have nonminimum-phase. To solve the problems of nonlinear distortions, two novel feedback adaptive filters based on the functional link neural network (FLNN) for NANC systems with low computational complexity are proposed in this paper, which are a feedback functional link neural network (FFLNN) and a reduced feedback functional link neural network (RFFLNN), respectively. To train the proposed nonlinear filters for NANC systems, a reduced complexity filtered-s least mean square (FSLMS) algorithm using filter bank approach is developed. The analysis of computational complexity shows that the RFFLNN adaptive filter involves less computation as compared to FFLNN and FLNN adaptive filters. Moreover, it is demonstrated through computer simulations for nonlinear noise processes that the RFFLNN adaptive filter outperforms FLNN and FFLNN in term of convergence speed and steady-state error. Furthermore, it is more effective in reducing nonlinear effects in NANC systems than other filters. [Copyright &y& Elsevier]

• In this paper, we propose a diffusion recursive total least squares (DRTLS) algorithm by using the single inverse power iterations in the distributed network. Further, to reduce the computational complexity of the DRTLS algorithm, an improved algorithm called DCD-DRTLS is also proposed by using the dichotomous coordinate descent (DCD) iterations. • we analyze the mean and mean square behaviors of the proposed DRTLS algorithm. • Simulation results illustrate the superiority of the proposed algorithms than other compared algorithms and the validity of the theoretical analysis results. In most existing distributed estimation algorithms, many scholars adopted the assumption that the output signal of the system is noisy and the input signal is sufficiently accurate. However, in real applications, the filter input vector usually contains noise. In such situations, it has been proved that the adaptive filtering algorithm using total least squares (TLS) method has shown better performance than classical least squares (LS) method. So in this paper, we propose a diffusion recursive total least squares (DRTLS) algorithm by using the single inverse power iterations in the distributed network. Then, we analyze the mean and mean square behaviors of the proposed DRTLS algorithm. In addition, to reduce the computational complexity of the DRTLS algorithm,an improved algorithm called DCD-DRTLS is also proposed by using the dichotomous coordinate descent (DCD) iterations. At last, simulation results illustrate the superiority of the proposed algorithms and the validity of the theoretical analysis results. [ABSTRACT FROM AUTHOR]

To ameliorate the performance of the normalized least mean square (NLMS) algorithm applied in identifying block-sparse system, a novel block-sparse proportionate NLMS (BS-PNLMS) algorithm based on the mixed l 2,0 norm is presented in this paper. The cost function of proposed algorithm is obtained by introducing the approximated mixed l 2,0 norm penalty in the cost function of BS-PNLMS algorithm, which is equivalent to attaching the mixed l 2,0 norm zero attraction to the update equation. The proposed algorithm is named as the l 2,0 -BS-PNLMS algorithm. Futhermore, a variable step-size l 2,0 -BS-PNLMS is developed to further improve the performance of the l 2,0 -BS-PNLMS. Simulation results demonstrate the advantages of proposed algorithms. [ABSTRACT FROM AUTHOR]

Two robust kernel adaptive filter (KAF) algorithms, called the kernel least mean p-power (KLMP) and kernel recursive least mean p-power (KRLP), are developed by combining mean p-power error (MPE) criterion and kernel trick for noisy chaotic time series prediction (CTSP). The proposed algorithms employ the MPE to overcome the performance degradation of the CTSP when training data are corrupted by impulsive noises (especially the α-stable noises). First, the KLMP algorithm is proposed by the gradient decent method to improve the robustness of the traditional kernel least mean square (KLMS). Second, the recursion idea and the kernel method are utilized to develop a recursive KAF, namely KRLP, to improve the robustness of the traditional kernel recursive least squares (KRLS). Simulation results show that the proposed algorithms display notable robustness in CTSP when the training data contain different levels of noises, and can perform better in terms of testing MSE than other algorithms. [ABSTRACT FROM AUTHOR]

In this brief, a robust and sparse recursive adaptive filtering algorithm, called convex regularized recursive maximum correntropy (CR-RMC), is derived by adding a general convex regularization penalty term to the maximum correntropy criterion (MCC). An approximate expression for automatically selecting the regularization parameter is also introduced. Simulation results show that the CR-RMC can significantly outperform the original recursive maximum correntropy (RMC) algorithm especially when the underlying system is very sparse. Compared with the convex regularized recursive least squares (CR-RLS) algorithm, the new algorithm also shows strong robustness against impulsive noise. The CR-RMC also performs much better than other LMS-type sparse adaptive filtering algorithms based on MCC. [ABSTRACT FROM AUTHOR]